Previous |  Up |  Next

Article

Keywords:
first order differential equation; delta-symmetric solution; periodic doubling bifurcations; symmetry-breaking bifurcations
Summary:
Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.
References:
[1] V. I. Arnold: Geometrical Methods in the Theory of Ordinary Differential Equations. Springer-Verlag: New York, Heidelberg, Berlin, 1982. (Russian original, Moscow, 1978.)
[2] W. M. Boothby: An Introduction to Difterentiable Manifolds and Riemannian Geometry. New York, Academic Press, 1975. MR 0426007
[3] A. Klíč: Period doubling bifurcations in a two-box model of the Brusselator. Aplikace matematiky 5, sv. 28, 1983, 335-343. MR 0712910
[4] J. W. Swift K. Wiesenfeld: Suppression of Period Doubling in Symmetric Systems. (unpublished).
[5] J. W. Swift K. Wiesenfeld: Suppression of Period Doubling in Symmetric Systems. Physical Review Letters, Vol. 52, No 9, 1984, 705-708. DOI 10.1103/PhysRevLett.52.705 | MR 0734140
[6] M. Field: Equivariant dynamical systems. Bull. AMS 76, 1970, 1314-1318. DOI 10.1090/S0002-9904-1970-12657-X | MR 0277850 | Zbl 0205.28204
[7] J. E. Marsden M. McCrocken: The Hopf Bifurcation and Its Applications. New York, Springer-Verlag, 1976. MR 0494309
Partner of
EuDML logo